The best season to visit Sikkim will to a great extent depend on what you are really interested in.
If you want to be assured of a clear sight of the snowy ranges as well as clear skies, then the best months to visit this region would be mid-October to mid of January (over the last three to four years it has been noticed that the monsoons even extend to the third week of October).
It does however tend to get cold in December and January. For trekking, I feel the months of October and November are the most suitable; March and April are also fine for trekking at altitudes less than 4000 metres but can be hampered by occasional heavy showers and hail. The sky is hazy in the month of March and April but this is amply compensated by the rhododendrons and other flowers in bloom.
Snow at high altitudes -4000 metres to 6000 metres- persists till May and therefore it is not possible to trek at these altitudes from December to May. If you are interested in alpine plants at altitudes above 3000 metres the best months to see them are August and September; no leeches to bother you and no sultry and wet weather because you are above the reach of the clouds.
You can come to the hills during the monsoons too. The rainy season should not deter visitors from coming to Sikkim. By the middle of June, the tourists have reduced to a trickle. But isn’t that the reason why you should come to the hill?: not for land up in a place teeming with noisy tourists elbowing each other to move around?
The monsoons batter Sikkim from mid-June to the end of September: It rains on and on for days together. The orchids and the flowers that bloom in spring wither away. But monsoons do not mean all gloom. Although the blue skies take on a grey and dreary hue in sharp contrast the hills turn lush green from dry brown. Clouds descend to the earth and also swirl up from the valley below as mist submerges the surroundings completely lending a surreal ambience.
The scent of the monsoon rain is intoxicating – a celebration. Even the normally stark high-altitude landscape is coaxed by the rains to take on a green attire. You come to the hills to escape the crowds but if you come during the season you get crowds that are bigger. During the monsoons, there is no din of the city noises and all you can hear is the continuous lullaby of the pitter-patter of rain on the rooftop For those who want to get away from it all and spend a quiet sleepy quiet holiday, a monsoon sojourn is definitely an experience worth trying
The winter season also should not discourage visitors from coming to Sikkim. Cloud-free skies and majestic views of the Kangchenjunga mountain range present breathtaking vistas. The air is crisp. The hills start quickly shedding their green attire and become brown but in sharp contrast, the paddy fields metamorphose to a golden hue glistening in the sunlight.
The cherry trees bloom in full glory. And you can savour Sikkim’s delicious world-famous Mandarin oranges During the monsoons and as late as mid-October the roads to Sikkim are plagued with landslides and can throw your travel plans awry. But during the winters you are assured of clear roads and can journey hassle-free. Various Buddhist festivals during this period brighten the melancholic monsoon ambience, heighten the senses and stir the soul.
If Buddhism holds your interest, then a visit in December is appropriate as the month is full of Buddhist festivals.